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Theorem 2rmorex 3282
 Description: Double restricted quantification with "at most one," analogous to 2moex 2343. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
2rmorex
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem 2rmorex
StepHypRef Expression
1 nfcv 2591 . . 3
2 nfre1 2893 . . 3
31, 2nfrmo 3011 . 2
4 rspe 2890 . . . . . 6
54ex 435 . . . . 5
65ralrimivw 2847 . . . 4
7 rmoim 3277 . . . 4
86, 7syl 17 . . 3
98com12 32 . 2
103, 9ralrimi 2832 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1870  wral 2782  wrex 2783  wrmo 2785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-eu 2270  df-mo 2271  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-rmo 2790 This theorem is referenced by:  2reu2  37998
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